teacher purchased 300 colored pencils for an upcoming project. The pencils she dered come in packs of 20 and packs of 30. She ordered 14 packs in all. ite a system of equations to find the number of 20-pencil packs (x) and 30 . incil packs (y) the art teacher ordered.

Define Variables: Let's denote the number of 20-pencil packs as x and the number of 30-pencil packs as y. We are given two pieces of information that will help us create a system of equations: 1. The teacher ordered a total of 14 packs. 2. The teacher purchased 300 colored pencils in total. From the first piece of information, we can write the equation: x + y = 14Create Equations: From the second piece of information, we know that the total number of pencils from the 20-pencil packs and the 30-pencil packs must add up to 300. This gives us the second equation: 20x + 30y = 300Solve System: Now we have a system of two equations with two variables: 1. x + y = 14 2. 20x + 30y = 300 We can solve this system using substitution or elimination. Let's use the elimination method. We can multiply the first equation by 20 to help eliminate one of the variables: 20(x + y) = 20(14) 20x + 20y = 280Eliminate Variable: We now have two new equations: 1. 20x + 20y = 280 2. 20x + 30y = 300 Subtract the first equation from the second equation to eliminate x: (20x + 30y) - (20x + 20y) = 300 - 280 10y = 20Solve for y: Divide both sides of the equation by 10 to solve for y: 10y / 10 = 20 / 10 y = 2Find x: Now that we have the value for y, we can substitute it back into the first equation to find x: x + y = 14 x + 2 = 14 x = 14 - 2 x = 12

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A teacher purchased $300$ colored pencils for an upcoming project. The pencils she ordered come in packs of $20$ and packs of $30$ . She ordered $14$ packs in all. Write a system of equations to find the number of $20$ -pencil packs $(x)$ and $30$ -pencil packs $(y)$ the art teacher ordered.

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Grade 8

Write linear functions: word problems

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Q. A teacher purchased

300

colored pencils for an upcoming project. The pencils she ordered come in packs of

20

and packs of

30

. She ordered

14

packs in all. Write a system of equations to find the number of

20

-pencil packs

(x)

and

30

-pencil packs

(y)

the art teacher ordered.

Define Variables: Let's denote the number of $20$ -pencil packs as $x$ and the number of $30$ -pencil packs as $y$ . We are given two pieces of information that will help us create a system of equations: $\newline$ $1$ . The teacher ordered a total of $14$ packs. $\newline$ $2$ . The teacher purchased $300$ colored pencils in total. $\newline$ From the first piece of information, we can write the equation: $\newline$ $x + y = 14$
Create Equations: From the second piece of information, we know that the total number of pencils from the $20$ -pencil packs and the $30$ -pencil packs must add up to $300$ . This gives us the second equation: $\newline$ $20x + 30y = 300$
Solve System: Now we have a system of two equations with two variables: $\newline$ $1$ . $x + y = 14$ $\newline$ $2$ . $20x + 30y = 300$ $\newline$ We can solve this system using substitution or elimination. Let's use the elimination method. We can multiply the first equation by $20$ to help eliminate one of the variables: $\newline$ $20(x + y) = 20(14)$ $\newline$ $20x + 20y = 280$
Eliminate Variable: We now have two new equations: $\newline$ $1$ . $20x + 20y = 280$ $\newline$ $2$ . $20x + 30y = 300$ $\newline$ Subtract the first equation from the second equation to eliminate $x$ : $\newline$ $(20x + 30y) - (20x + 20y) = 300 - 280$ $\newline$ $10y = 20$
Solve for y: Divide both sides of the equation by $10$ to solve for y: $\newline$ $\frac{10y}{10} = \frac{20}{10}$ $\newline$ $y = 2$
Find $x$ : Now that we have the value for $y$ , we can substitute it back into the first equation to find $x$ :
$x + y = 14$
$x + 2 = 14$
$x = 14 - 2$
$x = 12$